Finance 450 General Comments for Final Two Weeks Course Goals, CAPM, APT, and Haugen’s Model, Active vs. Passive Portfolio Management, and Comments on Valuation

Welcome Back from Thanksgiving Break! Good luck for the final two weeks of classes!

General Overview and Course Goals Give a man a fish, … Give a man a fish, … –and you feed him for a day; Teach a man to fish, … Teach a man to fish, … –and you feed for for a lifetime; Teach a man to think, … Teach a man to think, … –and he won’t have to eat fish every day!

Goal of the Course Not to teach you everything there is to know about analyzing securities (that would be impossible to do, given both the limited time available and the fact that the economic environment is constantly changing and evolving), Not to teach you everything there is to know about analyzing securities (that would be impossible to do, given both the limited time available and the fact that the economic environment is constantly changing and evolving), But to teach you how to think about the markets, so that you can be a more intelligent consumer of any investment advice you receive and a more critical reader of any future investment books you read (which I would anticipate and recommend that you do, since a lifetime of intelligent investing requires a lifetime of learning, and the more you read and learn, the better an investor you can be). But to teach you how to think about the markets, so that you can be a more intelligent consumer of any investment advice you receive and a more critical reader of any future investment books you read (which I would anticipate and recommend that you do, since a lifetime of intelligent investing requires a lifetime of learning, and the more you read and learn, the better an investor you can be).

Goal of the Course Also, a goal is to help provide a better foundation for those of you who are considering going on for their CFA charters. Also, a goal is to help provide a better foundation for those of you who are considering going on for their CFA charters. As such, the intended emphasis of this course is on aspects of investment analysis that aren’t covered in other finance classes and/or that are less readily accessible through self-study As such, the intended emphasis of this course is on aspects of investment analysis that aren’t covered in other finance classes and/or that are less readily accessible through self-study Hopefully, the course has been successful in this regard, and you have learned a lot! Hopefully, the course has been successful in this regard, and you have learned a lot! Additional comment: virtual portfolio project and English university system Additional comment: virtual portfolio project and English university system

Now, back to the lecture!

CAPM, APT, and Haugen’s Model All three of these provide expected-return factor models that can be used to predict expected returns for individual securities All three of these provide expected-return factor models that can be used to predict expected returns for individual securities –Can be used in conjunction with Markowitz optimization –Alternatively, these three models could be used to estimate the cost of equity capital for corporate financial management decisions But, each of the three models is fundamentally different from the other models But, each of the three models is fundamentally different from the other models

Asset Pricing Theories  Estimating expected return with the Asset Pricing Models of Modern Finance  CAPM: strong assumption -- strong prediction.

Expected Return Risk (Return Variability) Market Index on Efficient Set Market Index A B C Market Beta Expected Return Corresponding Security Market Line x x x x x x x x x x x x x x x x x x x x x x x x

Market Index Expected Return Risk (Return Variability) Market Index Inside Efficient Set Corresponding Security Market Cloud Expected Return Market Beta

CAPM and Roll’s Critique According to Richard Roll, the only testable implication of CAPM is that the true market portfolio is (mean- variance) efficient According to Richard Roll, the only testable implication of CAPM is that the true market portfolio is (mean- variance) efficient –i.e., CAPM implies M lies on the efficient frontier –all the other implications of CAPM, such as the SML, are a mathematical consequence of this and will follow naturally if the true market portfolio is efficient. But, the true market portfolio is unobservable (since it contains ALL risky assets) But, the true market portfolio is unobservable (since it contains ALL risky assets) –this leads to the problem of “benchmark error”, in which the index used as a proxy for the market portfolio does not perfectly match the true market portfolio –nor can we ever observe the true efficient frontier (it must always be estimated, and different assumptions will lead to different estimates)

CAPM and Roll’s Critique Thus, CAPM is ultimately untestable: Thus, CAPM is ultimately untestable: –If a linear relationship between beta and expected return is found, just shows that proxy index is mean- variance efficient, not necessarily that the true market portfolio is mean-variance efficient, –and vice versa Other effects of benchmark error: Other effects of benchmark error: –Beta would be wrong –The SML would be wrong

Arbitrage Pricing Theory (APT) CAPM is criticized by Roll because of the difficulties in selecting a proxy for the market portfolio as a benchmark CAPM is criticized by Roll because of the difficulties in selecting a proxy for the market portfolio as a benchmark An alternative pricing theory with fewer assumptions was developed by Stephen Ross: An alternative pricing theory with fewer assumptions was developed by Stephen Ross: Arbitrage Pricing Theory Arbitrage Pricing Theory

Arbitrage Pricing Theory - APT Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes

Assumptions of CAPM That Were Not Required by APT APT does not assume A market portfolio that contains all risky assets, and is mean-variance efficient A market portfolio that contains all risky assets, and is mean-variance efficient Normally distributed security returns Normally distributed security returns Quadratic utility function Quadratic utility function

Arbitrage Pricing Theory (APT) For i = 1 to N where: For i = 1 to N where: = return on asset i during a specified time period = expected return for asset i = reaction in asset i’s returns to movements in a common factor = a common factor with a zero mean that influences the returns on all assets = a unique effect on asset i’s return that, by assumption, is completely diversifiable in large portfolios and has a mean of zero = number of assets R i E i b ik N

Arbitrage Pricing Theory (APT) B ik determine how each asset reacts to this common factor Each asset may be affected by growth in GNP, but the effects will differ In application of the theory, the factors are not identified Similarly to CAPM, the unique effects are independent and will be diversified away in a large portfolio

Arbitrage Pricing Theory (APT) APT assumes that, in equilibrium, the return on a zero-investment, zero- systematic-risk portfolio is zero when the unique effects are diversified away APT assumes that, in equilibrium, the return on a zero-investment, zero- systematic-risk portfolio is zero when the unique effects are diversified away The expected return on any asset i (E i ) can be expressed as: The expected return on any asset i (E i ) can be expressed as:

Arbitrage Pricing Theory (APT) where: = the expected return on an asset with zero systematic risk where = the risk premium related to each of the common factors - for example the risk premium related to interest rate risk b i = the pricing relationship between the risk premium and asset i - that is how responsive asset i is to this common factor K

Example of Two Stocks and a Two-Factor Model = changes in the rate of inflation. The risk premium related to this factor is 1 percent for every 1 percent change in the rate = percent growth in real GNP. The average risk premium related to this factor is 2 percent for every 1 percent change in the rate = the rate of return on a zero-systematic-risk asset (zero beta: b oj =0) is 3 percent

Example of Two Stocks and a Two-Factor Model = the response of asset X to changes in the rate of inflation is 0.50 = the response of asset Y to changes in the rate of inflation is 2.00 = the response of asset X to changes in the growth rate of real GNP is 1.50 = the response of asset Y to changes in the growth rate of real GNP is 1.75

Example of Two Stocks and a Two-Factor Model =.03 + (.01)b i1 + (.02)b i2 =.03 + (.01)b i1 + (.02)b i2 E x =.03 + (.01)(0.50) + (.02)(1.50) E x =.03 + (.01)(0.50) + (.02)(1.50) =.065 = 6.5% =.065 = 6.5% E y =.03 + (.01)(2.00) + (.02)(1.75) E y =.03 + (.01)(2.00) + (.02)(1.75) =.085 = 8.5% =.085 = 8.5%

Arbitrage Pricing Theory (APT) Multiple factors expected to have an impact on all assets: –Inflation –Growth in GNP –Major political upheavals –Changes in interest rates –And many more…. Contrast with CAPM insistence that only beta is relevant

APT vs. CAPM In form, APT is similar to CAPM, but with multiple risk factors, rather than just one market risk factor, driving expected returns In form, APT is similar to CAPM, but with multiple risk factors, rather than just one market risk factor, driving expected returns In practice, APT appears to work better than CAPM In practice, APT appears to work better than CAPM But, while CAPM has Roll’s Critique, APT has Shanken’s Critique … But, while CAPM has Roll’s Critique, APT has Shanken’s Critique …

Shanken’s Challenge to Testability of the APT If returns are not explained by a model, it is not considered rejection of a model; however if the factors do explain returns, it is considered support If returns are not explained by a model, it is not considered rejection of a model; however if the factors do explain returns, it is considered support APT has no advantage because the factors need not be observable, so equivalent sets may conform to different factor structures APT has no advantage because the factors need not be observable, so equivalent sets may conform to different factor structures Empirical formulation of the APT may yield different implications regarding the expected returns for a given set of securities Empirical formulation of the APT may yield different implications regarding the expected returns for a given set of securities Thus, the theory cannot explain differential returns between securities because it cannot identify the relevant factor structure that explains the differential returns Thus, the theory cannot explain differential returns between securities because it cannot identify the relevant factor structure that explains the differential returns

The Arbitrage Pricing Theory  Estimating the macro-economic betas.  Obtain a characteristic line for each risk factor  Regress return on stock against risk factor

Relationship Between Return to General Electric and Changes in Interest Rates -25% -20% -15% -10% -5% 0% 5% 10% 15% 20% 25% Return to G.E. -10%-5%0%5%10% Percentage Change in Yield on Long-term Govt. Bond Line of Best Fit April, 1987

The Arbitrage Pricing Theory  Estimating the macro-economic betas.  No-arbitrage condition for asset pricing.  If risk-return relationship is non-linear, you can arbitrage.

Asset Pricing Theories  Estimating expected return with the Asset Pricing Models of Modern Finance  CAPM: strong assumption -- strong prediction.  APT: weak assumption -- weak prediction.

Curved Relationship Between Expected Return and Interest Rate Beta -15% -5% 5% 15% 25% 35% Expected Return -313 Interest Rate Beta A B C D E F

The Arbitrage Pricing Theory  Two stocks:  A: E(r) = 4%; Interest-rate beta =  B: E(r) = 26%; Interest-rate beta = 1.83  Invest 54.54% in E and 45.46% in A.  Portfolio E(r) =.5454 * 26% * 4% = 16%  Portfolio beta =.5454 * * = 0  With many combinations like this, you can create a risk-free portfolio with a 16% expected return.

The Arbitrage Pricing Theory  Two different stocks:  C: E(r) = 15%; Interest-rate beta =  D: E(r) = 25%; Interest-rate beta = 1.00  Invest 50.00% in E and 50.00% in A.  Portfolio E(r) =.5000 * 25% * 15% = 20%  Portfolio beta =.5000 * * = 0  With many combinations like this, you can create a risk-free portfolio with a 20% expected return. Then sell-short the 16% and invest the proceeds in the 20% to arbitrage.

The Arbitrage Pricing Theory  No-arbitrage condition for asset pricing.  If risk-return relationship is non-linear, you can arbitrage.  Attempts to arbitrage will force linearity in relationship between risk and return.

APT Relationship Between Expected Return and Interest Rate Beta -15% -5% 5% 15% 25% 35% Expected Return -313 Interest Rate Beta A B C D E F

The Arbitrage Pricing Theory  But, finite samples and fat-tailed distributions preclude the formation of the riskless hedges that are necessary to ensure that the theory holds  E.g., LTCM  More significantly, true risk factors never known for sure  Moreover, if markets are inefficient, then factors other than risk factors may also be important  This is the key contribution of Haugen

Haugen’s Approach Two components: Two components: –Risk factor model for modeling stocks’ risks and covariances for modeling stocks’ risks and covariances –Ad hoc expected return factor model for predicting stocks’ expected returns for predicting stocks’ expected returns allow both risk factors and non-risk factors allow both risk factors and non-risk factors Combine together using Markowitz portfolio optimization Combine together using Markowitz portfolio optimization

Probability Distribution For Returns to a Portfolio Possible Rates of Returns Probability Expected Return Variance of Return

Risk Factor Models The variance of stock returns can be split into two components: The variance of stock returns can be split into two components: l Variance = systematic risk + diversifiable risk l Systematic risk is modeled using an APT-type risk-factor model l Measures extent to which stocks’ returns [jointly] move up and down over time l Estimated using time-series data l Diversifiable risk is reduced through optimal diversification

Expected Return Factor Models Expected return factor models measure / predict the extent to which the stocks’ returns are different from each other within a given period of time. Expected return factor models measure / predict the extent to which the stocks’ returns are different from each other within a given period of time.

Expected Return Factor Models The factors in an expected return model represent the character of the companies. The factors in an expected return model represent the character of the companies. They might include the history of their stock prices, its size, financial condition, cheapness or dearness of prices in the market, etc. They might include the history of their stock prices, its size, financial condition, cheapness or dearness of prices in the market, etc. – Unlike CAPM and APT, not only risk factors such as market beta or APT betas are included Factor payoffs are estimated by relating individual stock returns to individual stock characteristics over the cross-section of a stock population (here the largest 3000 U.S. stocks). Factor payoffs are estimated by relating individual stock returns to individual stock characteristics over the cross-section of a stock population (here the largest 3000 U.S. stocks).

Five Factor Families Risk Risk – Market and APT betas, TIE, debt ratio, etc., values and trends thereof Liquidity Liquidity – Market cap., price, trading volume, etc. Price level Price level – E/P, B/P, Sales/P, CF/P, Div/P Profitability Profitability – Profit margin, ROE, ROA, earnings surprise, etc. Price history (technical factors) Price history (technical factors) – Excess return over past 1, 2, 3, 6, 12, 24, & 60 months

The Most Important Factors The monthly slopes (payoffs) are averages over the period 1979 through mid The monthly slopes (payoffs) are averages over the period 1979 through mid “T” statistics on the averages are computed, and the stocks are ranked by the absolute values of the “Ts”. “T” statistics on the averages are computed, and the stocks are ranked by the absolute values of the “Ts”.

Most Important Factors 1979/01 through 1986/ /07 through 1993/12 FactorMeanConfidenceMeanConfidence One-month excess return -0.97%99%-0.72%99% return Twelve-month excess 0.52%99%0.52%99% Trading volume/market cap-0.35%99%-0.20%98% Two-month excess return -0.20%99%-0.11%99% Earnings to price 0.27%99%0.26%99% Return on equity 0.24%99%0.13%97% Book to price 0.35%99%0.39%99% Trading volume trend -0.10%99%-0.09%99% Six-month excess return 0.24%99%0.19%99% Cash flow to price 0.13%99%0.26%99%

The Most Important Factors Among the factors that are significant (i.e., that can be used to distinguish between which companies will have higher returns and which will have lower returns) are: Among the factors that are significant (i.e., that can be used to distinguish between which companies will have higher returns and which will have lower returns) are: – A number of liquidity factors – Various fundamental factors, indicating value with growth – Technical factors, indicating short-term reversals and intermediate term momentum Suggest that technical factors provide marginal value when used in conjunction with fundamental analysis Suggest that technical factors provide marginal value when used in conjunction with fundamental analysis – Notably, no CAPM or APT risk factors are included!

The Great Race (From Ch. 13)

A Test of Relative Predictive Power Model employing factors exploiting the market’s tendencies to over- and under-react vs. Models employing risk factors only (“deductive” models of modern finance).

The Ad Hoc Expected Return Factor Model Risk Risk Liquidity Liquidity Profitability Profitability Price level Price level Price history Price history Earnings revision and surprise Earnings revision and surprise

Decile Returns for the Ad Hoc Factor Model (1980 through mid 1997) (1980 through mid 1997) Decile 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 1AverageAnnualized Return

The Capital Asset Pricing Model Market beta measured over the trailing 3 to 5-year periods). Market beta measured over the trailing 3 to 5-year periods). Stocks ranked by beta and formed into deciles monthly. Stocks ranked by beta and formed into deciles monthly.

Decile Returns for CAPM Model Decile 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 12AverageAnnualized Return

The Arbitrage Pricing Theory Macroeconomic Factors Macroeconomic Factors – Monthly T-bill returns – Long-term T-bond returns less short-term – T-bond returns less low-grade – Monthly inflation – Monthly change in industrial production Beta Estimation Beta Estimation – Betas re-estimated monthly by regressing stock returns on economic factors over trailing 3-5 years Payoff Projection Payoff Projection – Next month’s payoff is average of trailing 12 months

Average Returns for APT Model Annualized Decile 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 1AverageReturn

Overall Results Ad Hoc Expected Return Factor Model Ad Hoc Expected Return Factor Model – Average Annualized Spread Between Deciles 1 & % – Years with Negative Spreads 0 years Models Based on MODERN FINANCE Models Based on MODERN FINANCE – CAPM Average Annualized Spread Between Deciles 1 & % Average Annualized Spread Between Deciles 1 & % Years with Negative Spreads13 years Years with Negative Spreads13 years – APT Average Annualized Spread Between Deciles 1 & % Average Annualized Spread Between Deciles 1 & % Years with Negative Spreads 6 years Years with Negative Spreads 6 years

CAPM vs. APT vs. Haugen CAPM – one risk factor included in model CAPM – one risk factor included in model APT – multiple risk factors included in model APT – multiple risk factors included in model –More realistic and appears to work better than CAPM in applications Haugen’s model – multiple risk factors as well as non- risk factors potentially included Haugen’s model – multiple risk factors as well as non- risk factors potentially included –Actual model applied will vary over time as market conditions change –More adaptable in face of potential market inefficiencies –Appears to work much better than either CAPM or APT in practice!

Getting to Heaven and Hell in the Stock Market (From Ch. 14)

The Position of Portfolios in Abnormal Profit Space Efficient Market Line True Abnormal Profit Super Stocks Stupid Stocks Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit Space Efficient Market Line True Abnormal Profit InvestmentHeaven Stupid Stocks Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit Space Efficient Market Line True Abnormal Profit InvestmentHeaven InvestmentHell Priced Abnormal Profit

The Position of Portfolios in Abnormal Profit Space Efficient Market Line True Abnormal Profit InvestmentHeaven InvestmentHell Priced Abnormal Profit Can’t get to heaven by going around the corner You must go directly to heaven

How do you get to Investment Heaven? Three main steps in Haugen’s approach: – Use risk factor models to estimate variances and covariances – Use ad hoc expected return factor models to determine desired stock characteristics and estimate expected returns Cannot just screen sequentially (“going around the corner”) for stocks with the desired characteristics Cannot just screen sequentially (“going around the corner”) for stocks with the desired characteristics – Combine this information into optimal portfolios through Markowitz optimization